Theorems · Theorem · group theory
Subgroup.map_equiv_eq_comap_symm
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] (f : G ≃* N) (K : Subgroup G),
Subgroup.map (↑f) K = Subgroup.comap (↑f.symm) K- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- MulEquivstatement and proof · cited by 1,142
- MulEquiv.symmstatement · cited by 482
- Subgroup.mapstatement · cited by 301
- MonoidHomClass.toMonoidHomstatement · cited by 294
- Subgroup.comapstatement · cited by 154
- Subgroup.map_equiv_eq_comap_symm'proof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- Subgroup.comap_equiv_eq_map_symmproof · cited by 3
- IsGaloisGroup.mulEquivCongr_mapSubgroup_fixingSubgroupproof · cited by 1
- MulEquiv.normal_map_iffproof · cited by 1
- MulEquiv.map_torsionproof · cited by 1
- Subgroup.normalCore_eq_iInf_comap_conjproof · cited by 1
- Subgroup.comap_equiv_eq_map_symm'proof · cited by 0